Such a top is known from document DE 102 10 616 B4 and comprises a linkage, which comprises, for displacing a top cloth, a linkage, which is displaceable between a closed position for spanning a vehicle interior and a storage position for clearing the vehicle interior to the top. The linkage, in relation to a vertical longitudinal center plane of the top on both sides, includes a link arrangement, which comprises a main four-arm hinge mechanism being mounted, so as to be pivotable, at a main bearing that is fixed relative to the vehicle, said main four-arm hinge mechanism being formed from two main links, one of which constitutes a so-called main pillar. In each instance, via a pivot, a roof frame element is articulated to the two main links. Another roof frame element is linked to said roof frame element via another four-arm hinge arrangement, which includes two control links, the other roof frame element being arranged at the front in the closed position of the linkage and being adjacent to a front apron of the relevant vehicle. For displacing or pivoting the front roof frame element as against the roof frame element being linked to the main four-arm hinge mechanism, the link arrangement includes a coupling rod, which, on the one hand, is linked to one of the main links, and is linked, on the other hand, via an elongated hole, to one of the control links and, via a slot lever, to the rear roof frame element. Linking links via elongated holes and slot guides is at the expense of the stiffness of the system.